91Ó°ÊÓ

When we talk about the work done by friction, we're discussing how much energy the frictional force takes from a moving object until it stops. In physics, work is calculated as the force applied multiplied by the distance over which the force is applied. However, in friction's case, it always acts in the opposite direction of motion, so the work done is considered negative.

In our exercise, the work done by friction brings the moving block to a stop. The initial kinetic energy of the block is converted into heat energy by the frictional force. Hence, the work done by friction equals the block’s initial kinetic energy, which is \( -0.02 ext{ J} \). The negative sign indicates that friction is taking energy away from the block.

Kinetic energy is the energy that an object possesses due to its motion. It's calculated using the formula \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass and \( v \) is the velocity of the object. In simpler terms, the faster an object moves, or the heavier it is, the more kinetic energy it has.

In our case, the block starts with kinetic energy because it's moving at a speed of \( 0.4 ext{ m/s} \). With a mass of \( 0.25 ext{ kg} \), its initial kinetic energy can be calculated to be \( 0.02 ext{ J} \). The frictional force then works to convert this energy into heat, stopping the block in the process.

Frictional force is the resistance that one surface or object encounters when moving over another. In our exercise, this force acts between the block and the table surface, opposing the block's motion.

Frictional force is a crucial factor because it determines how quickly the block stops moving. The magnitude of this force can be calculated using \( f = \mu N \), where \( \mu \) is the coefficient of friction, and \( N \) is the normal force, typically equal to the object's weight on a horizontal surface. For our block, the frictional force was \( 0.245 ext{ N} \), which led to the block coming to a stop over a specific distance.

The coefficient of friction is a dimensionless number that represents the degree of interaction between two surfaces. A higher coefficient means more frictional force for a given normal force. In our problem, the coefficient of friction between the block and the table is \( 0.1 \).

This means that the surfaces experience a moderate degree of friction, not too high and not too low. It's used to calculate the frictional force and helps predict how far the block will slide before stopping. This calculation involves plugging the coefficient into the formula for frictional force \( f = \mu N \), turning kinetic energy into friction work until the block halts.